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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN"><!--Converted with LaTeX2HTML 97.1 (release) (July 13th, 1997) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan* with significant contributions from: Jens Lippman, Marek Rouchal, Martin Wilck and others --><HTML><HEAD><TITLE>5.4.5 Neural Gas with Competitive Hebbian Learning</TITLE><META NAME="description" CONTENT="5.4.5 Neural Gas with Competitive Hebbian Learning"><META NAME="keywords" CONTENT="DemoGNG"><META NAME="resource-type" CONTENT="document"><META NAME="distribution" CONTENT="global"><META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso_8859_1"><LINK REL="STYLESHEET" HREF="DemoGNG.css"><LINK REL="next" HREF="node20.html"><LINK REL="previous" HREF="node18.html"><LINK REL="up" HREF="node14.html"><LINK REL="next" HREF="node20.html"></HEAD><BODY ><!--Navigation Panel--><A NAME="tex2html290" HREF="node20.html"><IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="http://www.neuroinformatik.ruhr-uni-bochum.de/icons/next_motif.gif"></A> <A NAME="tex2html287" HREF="node14.html"><IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="http://www.neuroinformatik.ruhr-uni-bochum.de/icons/up_motif.gif"></A> <A NAME="tex2html281" HREF="node18.html"><IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="http://www.neuroinformatik.ruhr-uni-bochum.de/icons/previous_motif.gif"></A> <A NAME="tex2html289" HREF="node1.html"><IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="http://www.neuroinformatik.ruhr-uni-bochum.de/icons/contents_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html291" HREF="node20.html">5.4.6 Growing Neural Gas</A><B> Up:</B> <A NAME="tex2html288" HREF="node14.html">5.4 Model Specific Options</A><B> Previous:</B> <A NAME="tex2html282" HREF="node18.html">5.4.4 Competitive Hebbian Learning</A><BR><BR><!--End of Navigation Panel--><A NAME="tex2html1" HREF="http://www.neuroinformatik.ruhr-uni-bochum.de/ini/VDM/research/gsn/DemoGNG/NGwCHL_2.html">Neural Gas with Competitive Hebbian Learning</A><IMG WIDTH="49" HEIGHT="38" ALIGN="BOTTOM" BORDER="0" SRC="../smallDuke.gif"><H3><A NAME="SECTION00074500000000000000">5.4.5 </A></H3><DL><DT><STRONG>lambda_i</STRONG><DD>lambda initial (<IMG WIDTH="17" HEIGHT="26" ALIGN="MIDDLE" BORDER="0" SRC="img13.gif" ALT="$\lambda_i$">).<DT><STRONG>lambda_f</STRONG><DD>lambda final (<IMG WIDTH="20" HEIGHT="26" ALIGN="MIDDLE" BORDER="0" SRC="img14.gif" ALT="$\lambda_f$">).<DT><STRONG>epsilon_i</STRONG><DD>epsilon initial (<IMG WIDTH="14" HEIGHT="24" ALIGN="MIDDLE" BORDER="0" SRC="img10.gif" ALT="$\epsilon_i$">).<DT><STRONG>epsilon_f</STRONG><DD>epsilon final (<IMG WIDTH="17" HEIGHT="24" ALIGN="MIDDLE" BORDER="0" SRC="img11.gif" ALT="$\epsilon_f$">).<DT><STRONG>t_max</STRONG><DD>The simulation ends, if the number of input signalsexceed this value (<I>t</I><SUB><I>max</I></SUB>).<DT><STRONG>edge_i</STRONG><DD>Initial value for time-dependend edge aging (<I>T</I><SUB><I>i</I></SUB>).<DT><STRONG>edge_f</STRONG><DD>Final value for time-dependend edge aging (<I>T</I><SUB><I>f</I></SUB>).</DL>Edges are removed with an age larger than the maximal age <I>T</I>(<I>t</I>) whereby<P ALIGN="CENTER"><IMG WIDTH="158" HEIGHT="27" SRC="img19.gif" ALT="\begin{displaymath}T(t) = T_i(T_f/T_i) ^ {t/t_{\rm max}}.\end{displaymath}"></P>The reference vectors are adjusted according to<P ALIGN="CENTER"><IMG WIDTH="241" HEIGHT="26" SRC="img15.gif" ALT="\begin{displaymath}\Delta \mbox{\bf w}_i = \epsilon(t) \cdot h_\lambda(k_i(\mbo... ...$\xi$},{\cal A})) \cdot (\mbox{\boldmath$\xi$}- \mbox{\bf w}_i)\end{displaymath}"></P>with the following time-dependencies:<P ALIGN="CENTER"><IMG WIDTH="151" HEIGHT="27" SRC="img16.gif" ALT="\begin{displaymath}\lambda(t) = \lambda_i (\lambda_f/\lambda_i)^{t/t_{\rm max}}\end{displaymath}"></P><P ALIGN="CENTER"><IMG WIDTH="140" HEIGHT="27" SRC="img17.gif" ALT="\begin{displaymath}\qquad\epsilon(t) = \epsilon_i(\epsilon_f/\epsilon_i)^{t/t_{\rm max}}\end{displaymath}"></P><P ALIGN="CENTER"><IMG WIDTH="155" HEIGHT="26" SRC="img18.gif" ALT="\begin{displaymath}h_\lambda(k) = \exp(-k/\lambda(t)).\end{displaymath}"></P><BR><HR><ADDRESS><I>Hartmut S. Loos</I><BR><I>10/19/1998</I></ADDRESS></BODY></HTML>⌨️ 快捷键说明
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